# How do you solve 7x+1/-8=x-3/4?

Jan 26, 2017

See the entire solution process below:$x = - \frac{5}{48}$

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{8}$ to eliminate the fractions to make working with the equation easier and keep the equation balanced:

$\textcolor{red}{8} \times \left(7 x + \frac{1}{-} 8\right) = \textcolor{red}{8} \times \left(x - \frac{3}{4}\right)$

$\left(\textcolor{red}{8} \times 7 x\right) + \left(\textcolor{red}{8} \times \frac{1}{-} 8\right) = \left(\textcolor{red}{8} \times x\right) - \left(\textcolor{red}{8} \times \frac{3}{4}\right)$

$56 x + \frac{8}{-} 8 = 8 x - \frac{24}{4}$

$56 x - 1 = 8 x - 6$

Next, subtract $\textcolor{red}{8 x}$ and add $\textcolor{b l u e}{1}$ to each side of the equation to isolate the $x$ terms and keep the equation balanced:

$56 x - 1 - \textcolor{red}{8 x} + \textcolor{b l u e}{1} = 8 x - 6 - \textcolor{red}{8 x} + \textcolor{b l u e}{1}$

$56 x - \textcolor{red}{8 x} - 1 + \textcolor{b l u e}{1} = 8 x - \textcolor{red}{8 x} - 6 + \textcolor{b l u e}{1}$

$\left(56 - 8\right) x - 0 = 0 - 5$

$48 x = - 5$

Now, divide each side of the equation by $\textcolor{red}{48}$ to solve for $x$ while keeping the equation balanced:

$\frac{48 x}{\textcolor{red}{48}} = - \frac{5}{\textcolor{red}{48}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{48}}} x}{\cancel{\textcolor{red}{48}}} = - \frac{5}{48}$

$x = - \frac{5}{48}$